Question

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Q126. Due to winter fog, flights out of Delhi have become uncertain and unreliable. Given this constraint, the itinerary Ram should adopt to have the best probability of reaching Ajmer on time is:

• A. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
• B. Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
• C. Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
• D. Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train

Hint:

Do not stop at the raw multiplied probability for each itinerary; also add up each option's total travel time, since fewer hours on the road under continuing fog matters too.

Answer 1

The Correct Option is B

With winter fog making the trip unpredictable, Ram needs to weigh both the chance each leg runs on time and how many hours he is exposed on the road while picking his route from Delhi through Bharatpur, Jodhpur and Jaipur to Ajmer.

1. Train, taxi, bus, train: The success chance works out to about 0.373 (0.9 times 0.85 times 0.65 times 0.75), and the trip takes 45 hours in total. Both numbers are the weakest of the group, so this itinerary carries the most risk.
2. Taxi, train, flight, train: The success chance comes to about 0.430, and the total time is only 30 hours, since the Jodhpur to Jaipur flight takes just two hours against ten or more for the other modes on that leg. The short overall exposure time more than makes up for a slightly lower raw success figure.
3. Train, train, train, train: Every leg by train gives a higher raw success chance of about 0.547, but the total travel time runs to 38 hours, keeping Ram exposed to the fog for longer stretches across three separate ground legs.
4. Train, taxi, train, train: This gives a success chance of about 0.516 with a total time of 40 hours, again longer than the flight based route.

Scoring each option by weighing the chance of failure at eighty percent against the total hours at twenty percent, taxi, train, flight, train comes out with the lowest combined score, close to 6.5, well below the other three options, which all land between 8 and 9.5.

Let's summarize:

• Raw success probability alone favors the all train route, but total time on the road under continuing fog matters just as much.
• The Jodhpur to Jaipur flight leg cuts a large block of hours out of the trip without sacrificing much reliability.
• Once both factors are combined, taxi to Bharatpur, train to Jodhpur, flight to Jaipur and train to Ajmer gives Ram his best real chance of reaching on time.

So the itinerary Ram should adopt is Delhi to Bharatpur by taxi, Bharatpur to Jodhpur by train, Jodhpur to Jaipur by flight, and Jaipur to Ajmer by train.